The Hornets led for much of the encounter thanks to Andre Carrillo's early opener, but were left stunned as the troubled Swans hit back in the final five minutes of the game - first through Jordan Ayew, then Luciano Narsingh - to grab all three points.
The result marked just the fourth victory for the Welsh side all season and helped them off the bottom of the table in what was Carvalhal's first match in the dugout.
"[It was] a difficult game. Watford have a good team," Carvalhal told Match of the Day afterwards. "We deserved a win, luck is part of the game. We tried everything to win. Watford are very strong. We felt a little lucky in moments, but Watford were lucky also.
"The game is like this, but we prepared very well, changed the formation and had just two training sessions with the team. With two attackers, we were more open to try and create problems for Watford.
"I must give congratulations to my players. They are better players than they are showing. They need a plan and a dynamic. During the game they were better and better."
Next up for Swansea is a tough home encounter with Tottenham Hotspur on Tuesday evening.